2026-04-13T03:13:21Zhttps://recercat.cat/oai/request

oai:recercat.cat:10230/360162025-12-18T01:22:05Zcom_2072_6col_2072_452952

00925njm 22002777a 4500 dc Scarlett, Jonathan author Peng, Li author Merhav, Neri author Martínez, Alfonso, 1973- author Guillén i Fábregas, A. (Albert) author 2018-12-07T14:53:10Z 2018-12-07T14:53:10Z 2014 This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory. This work was supported in part by the European Research Council under Grant 259663, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150 and Grant TEC2012-38800-C03-03. The work of N. Merhav was supported by the Israel Science Foundation under Grant 412/12. Expurgated error exponents Reliability function Random coding Mismatched decoding Maximum-likelihood decoding Type class enumeration Expurgated random-coding ensembles: exponents, refinements and connections